Statistical Mechanics of Polymer Stretching

The interplay between Physics and Biology is certainly one of the most exciting field in modern Science. In particular, the discovery that proteins, DNA and RNA have rather peculiar spatial arrangements [1, 2, 3] has convinced biological physicists that these simple forms may be deduced from an underlying principle. Besides, new experimental techniques have supplied high-quality data, which can be investigated and compared to theoretical models. In particular, in this Thesis, we have focused our attention on the theoretical study of some elastic and thermodynamic properties of polymers and, in particular, biopolymers such as proteins, DNA and RNA [4]. This research work is organized as follows: In Chap. 1, we introduce some basic concept on polymers and biopolymers. In particular, biopolymers has attracted the attention of many research groups. Probably, their most appealing property is that they are organized in simple hierarchical structures [5]. In fact, the primary amino acid sequence of proteins is disposed in some fascinating forms as alpha-helices and beta-strands, which at an outer level form compact structures called domains. Moreover, 50 years ago, Watson and Crick [2] discovered the marvelous double helix of DNA. Furthemore, polymers seem to display many intriguing features, since they can not be described in terms of ordinary solids. This is due to the covalent nature of the bonds between consecutive monomers. Due to temperature fluctuations of these bonds, a polymer can not be viewed as a rigid macromolecule. Since these fluctuations favor many different spatial conformation, a Statistical Mechanics approach has revealed very useful [3]. Then, we focus on the important problem of polymer elasticity and introduce some preliminary concepts as the Kuhn length and the persistence length [4]. In Chap. 2, we focus our attention about some recent experiments on polymer stretching. Firstly, we begin with a brief introduction to some recent experimental techniques. Mainly, we focus on optical tweezers [6], atomic force microscopes [7] and soft microneedles [8]. We also give a short explanation about their technical features, including practical limitations and available force ranges. Besides, we describe in great details many force driven phase transition which occur in real polymers. Then, Statistical Mechanics allows for a rigorous approach to these phenomena. As explained above, we also address the important problem of elasticity in polymers, introducing the freely jointed chain (FJC) model and the worm like chain (WLC) model [3]. In Chap. 3, we describe the stretching behaviour of polymers, with the introduction of some chosen 2d on-lattice models and 3d off-lattice models. In the framework of a simplified approach on a self-interacting directed selfavoiding walk (DSAW) [9], we have discussed the importance of some scaling laws that we think to be of more general validity. Then, we introduce a more realistic model for a self-interacting SAW [9]. In particular we are able to describe its phase diagram. Through the introduction of an off-lattice self-avoiding polymer, we also give a simple explanation of some recent puzzling experimental results described in Chap. 2. In Chap. 4, we shall focus our attention on the stretching behaviour of polymer in a good solvent [10]. Generalizing the WLC approach of Marko and Siggia [11], we obtain a new interpolation formula, which perfectly describes some numerical data, obtained with Monte Carlo simulations. Furthermore, this formula seems to be more powerful than Marko and Siggia\u2019s one. In fact, it fits well some experimental data taken from literature, that the previous approach was not able to describe correctly. Finally, we outline final conclusions and perspectives

Breakdown of the Onsager principle as a sign of aging

We discuss the problem of the equivalence between Continuous Time Random Walk (CTRW) and Generalized Master Equation (GME). The walker, making instantaneous jumps from one site of the lattice to another, resides in each site for extended times. The sojourn times have a distribution psi(t) that is assumed to be an inverse power law. We assume that the Onsager principle is fulfilled, and we use this assumption to establish a complete equivalence between GME and the Montroll-Weiss CTRW. We prove that this equivalence is confined to the case when psi(t) is an exponential. We argue that is so because the Montroll-Weiss CTRW, as recently proved by Barkai [E. Barkai, Phys. Rev. Lett. 90, 104101 (2003)], is non-stationary, thereby implying aging, while the Onsager principle, is valid only in the case of fully aged systems. We consider the case of a dichotomous fluctuation, and we prove that the Onsager principle is fulfilled for any form of regression to equilibrium provided that the stationary condition holds true. We set the stationary condition on both the CTRW and the GME, thereby creating a condition of total equivalence, regardless the nature of the waiting time distribution. As a consequence of this procedure we create a GME that it is a "bona fide" master equation, in spite of being non-Markovian. We note that the memory kernel of the GME affords information on the interaction between system of interest and its bath. The Poisson case yields a bath with infinitely fast fluctuations. We argue that departing from the Poisson form has the effect of creating a condition of infinite memory and that these results might be useful to shed light into the problem of how to unravel non-Markovian master equations.Comment: one file .tex, revtex4 style, 11 page

Multi-scale modeling of diffusion-controlled reactions in polymers: Renormalisation of reactivity parameters

The quantitative description of polymeric systems requires hierarchical modeling schemes, which bridge the gap between the atomic scale, relevant to chemical or biomolecular reactions, and the macromolecular scale, where the longest relaxation modes occur. Here, we use the formalism for diffusion-controlled reactions in polymers developed by Wilemski, Fixman, and Doi to discuss the renormalisation of the reactivity parameters in polymer models with varying spatial resolution. In particular, we show that the adjustments are independent of chain length. As a consequence, it is possible to match reactions times between descriptions with different resolution for relatively short reference chains and to use the coarse-grained model to make quantitative predictions for longer chains. We illustrate our results by a detailed discussion of the classical problem of chain cyclization in the Rouse model, which offers the simplest example of a multi-scale descriptions, if we consider differently discretized Rouse models for the same physical system. Moreover, we are able to explore different combinations of compact and non-compact diffusion in the local and large-scale dynamics by varying the embedding dimension. Z9

Structure and microrheology of genome organization: From experiments to physical modeling.

The mechanisms beyond chromosome folding within the nuclei of eukaryotic cells have fundamental implications in important processes like gene expression and regulation. Yet, they remain widely unknown. Unveiling the secrets of nuclear processes requires a cross-disciplinary approach combining experimental techniques to theoretical, mathematical and physical modeling. In this review, we discuss our current understanding of the generic aspects of genome organization during interphase in terms of the conceptual connection between the large-scale structure of chromosomes and the physics beyond the crumpled structure of entangled ring polymers in solution. Then, we employ this framework to discuss recent experimental and theoretical results for microrheology of Brownian nanoprobes dispersed in the nuclear medium

Nanoprobe diffusion in entangled polymer solutions: Linear vs. unconcatenated ring chains

We employ large-scale molecular dynamics computer simulations to study the problem of nanoprobe diffusion in entangled solutions of linear polymers and unknotted and unconcatenated circular (ring) polymers. By tuning both the diameter of the nanoprobe and the density of the solution, we show that nanoprobes of diameter smaller than the entanglement distance (tube diameter) of the solution display the same (Rouse-like) behavior in solutions of both polymer architectures. Instead, nanoprobes with larger diameters appear to diffuse markedly faster in solutions of rings than in solutions of linear chains. Finally, by analysing the distribution functions of spatial displacements, we find that nanoprobe motion in rings' solutions shows both Gaussian and ergodic behaviors, in all regimes considered, while, in solutions of linear chains, nanoprobes exceeding the size of the tube diameter show a transition to non-Gaussian and non-ergodic motion. Our results emphasize the role of chain architecture in the motion of nanoprobes dispersed in polymer solutions

Efficacy of acoustic waves in preventing Streptococcus mutans adhesion on dental unit water line

Background: nei riuniti odontoiatrici, la qualità dell'acqua utilizzata per la refrigerazione e il risciacquo di manipoli, siringhe e altri componenti è un aspetto di notevole importanza sanitaria. L'acqua attraversa questi dispositivi mediante un circuito interconnesso di tubi di piccole dimensioni (circa 2 mm di diametro), denominato “dental unit water line” (DUWL). I DUWL possono essere fortemente colonizzati da varie specie batteriche sia in fase planctonica, che adesi o organizzati in biofilm, rappresentando una potenziale causa di infezione, non solo per i professionisti che usano abitualmente questi dispositivi, ma anche per pazienti occasionali, in particolare per i pazienti immunocompromessi. La contaminazione dei DUWL può essere prevenuta o ridotta con l'uso dei disinfettanti, ma l'eradicazione dei microrganismi adesi alle superfici interne dei DUWL o organizzati in forma di biofilm, è una sfida assai più complessa e spesso i normali metodi di disinfezione non sono pienamente efficaci. Inoltre, in ambito odontoiatrico, i disinfettanti utilizzati abitualmente per disinfettare i DUWL possono alterare la capacità adesiva del materiale utilizzato nella pratica restaurativa. Obiettivi: individuare una strategia innovativa, in grado di contrastare l'adesione batterica alle superfici dei DUWL mediante un approccio di tipo fisico, che sia più efficace nel superare il problema della contaminazione dei DUWL e ridurre il rischio di infezione rispetto ai normali metodi già in uso. A tal fine, fra le molte specie batteriche potenzialmente riscontrabili nei circuiti idrici odontoiatrici, si è deciso di avviare questo studio pilota utilizzando la specie batterica patogena S. mutans, per il suo indubbio interesse in ambito odontoiatrico e per la sua spiccata capacità di aderire e persistere su superfici inerti. Metodi: utilizzo di onde acustiche elastiche ad alta energia nel contrastare l'adesione di Streptococcus mutans alle pareti interne di un circuito idrico sperimentale riproducente un DUWL. Per evidenziare l’efficacia delle onde acustiche anche in condizioni estreme, è stata utilizzata un’elevata carica contaminante di S. mutans. Risultati: Si osserva una significativa riduzione dei batteri adesi soggetti a trattamento con onde acustiche rispetto al controllo (P = 0,003)

Randomly branching theta-polymers in two and three dimensions: Average properties and distribution functions

Motivated by renewed interest in the physics of branched polymers, we present here a detailed characterization of the connectivity and spatial properties of 2- and 3-dimensional single-chain conformations of randomly branching polymers under theta-solvent conditions obtained by Monte Carlo computer simulations. The first part of the work focuses on polymer average properties, such as the average polymer spatial size as a function of the total tree mass and the typical length of the average path length on the polymer backbone. In the second part, we move beyond average chain behavior and we discuss the complete distribution functions for tree paths and tree spatial distances, which are shown to obey the classical Redner-des Cloizeaux functional form. Our results were rationalized first by the systematic comparison to a Flory theory for branching polymers and next by generalized Fisher-Pincus relationships between scaling exponents of distribution functions. For completeness, the properties of theta-polymers were compared to their ideal (i.e., no volume interactions) as well as good-solvent (i.e., above the theta-point) counterparts. The results presented here complement the recent work performed in our group [A. Rosa and R. Everaers, J. Phys. A: Math. Theor. 49, 345001 (2016); J. Chem. Phys. 145, 164906 (2016); and Phys. Rev. E 95, 012117 (2017)] in the context of the scaling properties of branching polymers

Topological analysis and the recovery of entanglements in polymer melts

The viscous flow of polymer chains in dense melts is dominated by topological constraints whenever the single chain contour length, N, becomes larger than the characteristic scale Ne, defining comprehensively the macroscopic rheological properties of the highly entangled polymer systems. Even though the latter are naturally connected to the presence of hard constraints like knots and links within the polymer chains, the difficulty of integrating the rigorous language of mathematical topology with the physics of polymer melts has limited somehow a genuine topological approach to the problem of classifying these constraints and to how they are related to the rheological entanglements. In this work, we tackle this problem by studying the occurrence of knots and links in lattice melts of randomly knotted and randomly concatenated ring polymers of various bending stiffness. Specifically, by introducing an algorithm which shrinks the chains to their minimal shapes which do not violate topological constraints and by analyzing those in terms of suitable topological invariants, we provide a detailed characterization of the topological properties at the intra-chain level (knots) and of links between pairs and triplets of distinct chains. Then, by employing the Z1-algorithm on the minimal conformations in order to extract the entanglement length $N_e$, we show that the ratio $N/N_e$, the number of entanglements per chain, can be remarkably well reconstructed in terms of 2-chain links solely.Comment: Main: 9 pages, 6 figures. 6 supplementary figures. Submitted for publicatio

Spatial organization of slit-confined melts of ring polymers with non-conserved topology: A lattice Monte Carlo study

We present Monte Carlo computer simulations for melts of semiflexible randomly knotted and randomly concatenated ring polymers on the fcc lattice and in slit confinement. Through systematic variation of the slit width at fixed melt density, we first explore the influence of confinement on single-chain conformations and inter-chain interactions. We demonstrate that confinement makes chains globally larger and more elongated, while enhancing both contacts and knottedness propensities. As for multi-chain properties, we show that ring-ring contacts decrease with the confinement, yet neighbouring rings are more overlapped as confinement grows. These aspects are reflected on the decrease of the links formation between pairs of rings. The results suggest that confinement can be used to fine-tune the mechanical properties of the polymer network. In particular, confinement biases the synthesis of networks that are softer to mechanical stress. Finally, in connection with a previous study of us and recent simulations on two-dimensional polymer melts, our findings suggest that entanglements in polymer melts arise from pairwise ring-ring links alone.Comment: 11 pages, 8 figures. 5 supplementary figures. Submitted for publicatio